Standard form of the equation of parabola

In summary, the conversation is about finding the equation of a parabola with an axis of symmetry y=0 and focus(-5,0). The student is unsure how to approach the problem and asks for guidance. The expert clarifies that the equation will be in the form x = ay^2 + by + c and suggests looking for similar examples in the textbook to make connections.
  • #1
jOANIE
6
0

Homework Statement



Write the equation in standard form for the parabola with an axis of symmetry y=0 and focus(-5,0).

Homework Equations


I think ax^2+bx+c. Also maybe x = -b/2a. But I don't know how to apply these.



The Attempt at a Solution


I know that focus and vertex lie on axis of symmetry and that directrix ane axis of symmetry are perpendicular to each other.

If you could give me a similar example worked out, I would be able to do this one. Thanks.
 
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  • #2
jOANIE said:

Homework Statement



Write the equation in standard form for the parabola with an axis of symmetry y=0 and focus(-5,0).

Homework Equations


I think ax^2+bx+c.
I think not. First off, that's not an equation. Second, the axis of symmetry is the line y = 0 (the x-axis). This means that the equation will be x = ay^2 + by + c.
jOANIE said:
Also maybe x = -b/2a. But I don't know how to apply these.
x = -b/(2a) isn't the equation of a parabola; it gives you the x-coordinate of the vertex for a parabola that opens up or down. Your parabola opens left or right.
jOANIE said:

The Attempt at a Solution


I know that focus and vertex lie on axis of symmetry and that directrix ane axis of symmetry are perpendicular to each other.

If you could give me a similar example worked out, I would be able to do this one. Thanks.

Based on the information you provided, there are an infinite number of parabolas that satisfy these conditions. Aren't there any examples showing how to do this in your textbook?
 
  • #3
Hello--Thanks for responding. I cannot find an example like this one in my book. Could you give me any hints on how to begin this problem? I am completely self-taught in math and am trying to understand conics, which I have not attempted before. I am also good at following examples and, actually, learn quite a bit from them.
 
  • #4
OK, what's the example that seems the closest? Are there any examples where you're supposed to find the equation of a parabola of any kind? Maybe we can help you make some connections.
 

FAQ: Standard form of the equation of parabola

What is the standard form of the equation of a parabola?

The standard form of the equation of a parabola is y = ax^2 + bx + c, where a, b, and c are constants and a is not equal to 0.

How do you determine the direction and shape of a parabola using the standard form?

The value of a in the standard form equation determines the direction and shape of the parabola. If a is positive, the parabola opens upwards and has a "U" shape. If a is negative, the parabola opens downwards and has an "n" shape.

What do the constants b and c represent in the standard form equation?

The constant b represents the horizontal shift of the parabola, while the constant c represents the vertical shift. If b is positive, the parabola shifts to the left, and if b is negative, the parabola shifts to the right. Similarly, if c is positive, the parabola shifts upwards, and if c is negative, the parabola shifts downwards.

How do you graph a parabola using the standard form equation?

To graph a parabola using the standard form equation, you can use the x-intercepts and y-intercept. The x-intercepts are where the parabola crosses the x-axis, and they can be found by setting y to 0 and solving for x. The y-intercept is where the parabola crosses the y-axis, and it can be found by setting x to 0 and solving for y. Once you have the intercepts, you can plot them on a graph and draw a smooth curve connecting them to create the parabola.

How is the standard form of the equation of a parabola different from the vertex form?

The standard form and vertex form are two different ways of writing the equation of a parabola. The standard form y = ax^2 + bx + c shows the parabola in its general form, while the vertex form y = a(x-h)^2 + k shows the parabola in its vertex form. The constants h and k represent the coordinates of the vertex of the parabola.

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